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Quantitative Model Checking of Continuous-Time Markov Chains Against Timed Automata Specifications

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4 Author(s)

We study the following problem: given a continuous-time Markov chain (CTMC) C, and a linear real-time property provided as a deterministic timed automaton (DTA) A, what is the probability of the set of paths of C that are accepted by A (C satisfies A)? It is shown that this set of paths is measurable and computing its probability can be reduced to computing the reachability probability in a piecewise deterministic Markov process (PDP). The reachability probability is characterized as the least solution of a system of integral equations and is shown to be approximated by solving a system of partial differential equations. For the special case of single-clock DTA, the system of integral equations can be transformed into a system of linear equations where the coefficients are solutions of ordinary differential equations.

Published in:

Logic In Computer Science, 2009. LICS '09. 24th Annual IEEE Symposium on

Date of Conference:

11-14 Aug. 2009